Question

Write the equation of an ellipse with vertices at (7, 0) and (-7, 0) and co-vertices at (0, 1) and (0, -1).

Answer 1

Answer:

$\frac{(x)^{2}}{49}+\frac{(y)^{2}}{1}=1$

Step-by-step explanation:

In this problem we have a horizontal ellipse, because the major axis is the x-axis

The equation of a horizontal ellipse is equal to

$\frac{(x-h)^{2}}{a^{2}}+\frac{(y-k)^{2}}{b^{2}} =1$

where

(h,k) is the center of the ellipse

a and b  are the respective vertices distances from center

we have

vertices at (7, 0) and (-7, 0)

co-vertices at (0, 1) and (0, -1)

so

The center is the origin (0.0) (The center is the midpoint of the vertices)

a=7

b=1

substitute

$\frac{(x-0)^{2}}{7^{2}}+\frac{(y-0)^{2}}{1^{2}}=1$

$\frac{(x)^{2}}{49}+\frac{(y)^{2}}{1}=1$